Question : A man travels 434 km, partly by train and partly by steamer. He spends 8 hours more time on the steamer. If the velocity of the steamer is 25 km/hr and the velocity of the train is 65 km/hr, how much distance does he cover by steamer?
Option 1: 318 km
Option 2: 398 km
Option 3: 265 km
Option 4: 477 km
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Correct Answer: 265 km
Solution :
Let the time spent on the train be $x$ hours
and the time spent on the steamer is $(x+8)$ hours.
So, the distances travelled by train and steamer are $65x$ km and $25(x+8)$ km, respectively.
According to the question,
$65x + 25(x+8) = 434$
⇒ $90x = 234$
⇒ $x = \frac{234}{90}$ hours
Then, the time spend on the steamer is = ($\frac{234}{90}+8) = \frac{954}{90}$ hours
$\therefore$ The distance covered by him on the steamer is = ($\frac{954}{90}×25) = 265$ km
Hence, the correct answer is 265 km.
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